Equivalent Circuit Model of Lumped Elements Retrieved from Measured S-Parameters of Microstrip Line in Frequency Range 0.5-5GHz

Lumped elements always show a different frequency response from ideal ones when they work at higher frequencies such as microwave band, therefore they have to be modeled by equivalent circuits. To derive the circuit by experiments, we considered the lumped elements as a two-port network which was inserted into a microstrip transmission line for measurements. The network was first modeled as a general PI circuit first, and then finalized by the measured S-parameters. The method was applied to a surface-mounted device (SMD) resistor, a varactor diode, and a phototransistor working at the frequencies of 0.5-5 GHz. The derived circuit models were verified by their simulated S-parameters, which were in a very good agreement with the experiments. Our method provides a simple and effective way to build circuit models for lumped elements, which is helpful for their applications at microwave frequency. Specifically, our circuit model shows how the phototransistor changes its response under different illumination, which provides a way to use it in light-tunable devices.